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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 355 · 40 questions
TalentJR

How to solve it (180 is the magic number): The three angles of a triangle add up to 180°. An exterior angle equals the sum of the two interior angles opposite it. An isosceles triangle has two equal angles, opposite its two equal sides. Angles on a straight line add up to 180°; vertically opposite angles are equal.

NameDateTime takenScore ___ / 40
  1. 1.Two angles of a triangle are 20° and 145°. What is the third angle? (a) 165° (b) 35° (c) 15° (d) 160°
  2. 2.Two angles of a triangle are 20° and 75°. What is the third angle? (a) 160° (b) 95° (c) 105° (d) 85°
  3. 3.Two angles of a triangle are 20° and 70°. What is the third angle? (a) 160° (b) 270° (c) 90° (d) 110°
  4. 4.Two angles of a triangle are 45° and 20°. What is the third angle? (a) 65° (b) 115° (c) 160° (d) 135°
  5. 5.Two angles of a triangle are 45° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 100° (c) 80° (d) 135°
  6. 6.Two straight lines cross. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 110° (b) 220° (c) 70° (d) 40°
  7. 7.Two angles of a triangle are 40° and 30°. What is the third angle? (a) 110° (b) 150° (c) 140° (d) 70°
  8. 8.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 15° (b) 16° (c) 165° (d) 195°
  9. 9.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 75° (b) 76° (c) 150° (d) 105°
  10. 10.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 310° (b) 50° (c) 40° (d) 130°
  11. 11.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 15° (b) 75° (c) 105° (d) 30°
  12. 12.Two straight lines cross. One of the angles is 145°. What is the angle next to it on the same straight line? (a) 35° (b) 36° (c) 145° (d) 215°
  13. 13.Two straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 66° (b) 65° (c) 115° (d) 245°
  14. 14.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 16° (b) 165° (c) 30° (d) 15°
  15. 15.Two angles of a triangle are 70° and 40°. What is the third angle? (a) 140° (b) 110° (c) 250° (d) 70°
  16. 16.Two angles of a triangle are 30° and 120°. What is the exterior angle at the third corner? (a) 150° (b) 60° (c) 210° (d) 30°
  17. 17.Two angles of a triangle are 35° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 145° (c) 60° (d) 120°
  18. 18.Two angles of a triangle are 30° and 115°. What is the exterior angle at the third corner? (a) 35° (b) 150° (c) 145° (d) 65°
  19. 19.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 100° (b) 80° (c) 10° (d) 20°
  20. 20.Two angles of a triangle are 35° and 60°. What is the exterior angle at the third corner? (a) 145° (b) 120° (c) 85° (d) 95°
  21. 21.Two angles of a triangle are 35° and 30°. What is the third angle? (a) 145° (b) 65° (c) 115° (d) 150°
  22. 22.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 315° (b) 136° (c) 135° (d) 45°
  23. 23.Two angles of a triangle are 70° and 20°. What is the exterior angle at the third corner? (a) 110° (b) 160° (c) 90° (d) 270°
  24. 24.Two angles of a triangle are 35° and 80°. What is the exterior angle at the third corner? (a) 100° (b) 115° (c) 65° (d) 145°
  25. 25.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 35° (b) 45° (c) 70° (d) 110°
  26. 26.Two angles of a triangle are 70° and 60°. What is the exterior angle at the third corner? (a) 110° (b) 50° (c) 130° (d) 120°
  27. 27.Two angles of a triangle are 25° and 100°. What is the third angle? (a) 80° (b) 155° (c) 125° (d) 55°
  28. 28.Two angles of a triangle are 60° and 85°. What is the exterior angle at the third corner? (a) 145° (b) 120° (c) 35° (d) 95°
  29. 29.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 140° (b) 50° (c) 100° (d) 40°
  30. 30.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 300° (b) 120° (c) 60° (d) 30°
  31. 31.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 45° (b) 46° (c) 90° (d) 135°
  32. 32.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 120° (b) 30° (c) 70° (d) 60°
  33. 33.Two angles of a triangle are 35° and 30°. What is the exterior angle at the third corner? (a) 65° (b) 115° (c) 150° (d) 145°
  34. 34.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 205° (b) 26° (c) 155° (d) 25°
  35. 35.Two angles of a triangle are 40° and 20°. What is the exterior angle at the third corner? (a) 120° (b) 140° (c) 60° (d) 160°
  36. 36.Two straight lines cross. Two vertically opposite angles add up to 290°. What is each of the other two angles? (a) 70° (b) 36° (c) 35° (d) 145°
  37. 37.Two angles of a triangle are 75° and 50°. What is the third angle? (a) 105° (b) 55° (c) 130° (d) 125°
  38. 38.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 260° (b) 50° (c) 80° (d) 130°
  39. 39.Two angles of a triangle are 50° and 20°. What is the exterior angle at the third corner? (a) 110° (b) 130° (c) 160° (d) 70°
  40. 40.Two angles of a triangle are 25° and 135°. What is the third angle? (a) 45° (b) 160° (c) 155° (d) 20°

Answer key

  1. 15°
  2. 85°
  3. 90°
  4. 115°
  5. 80°
  6. 110°
  7. 110°
  8. 15°
  9. 75°
  10. 130°
  11. 30°
  12. 35°
  13. 65°
  14. 15°
  15. 70°
  16. 150°
  17. 60°
  18. 145°
  19. 20°
  20. 95°
  21. 115°
  22. 135°
  23. 90°
  24. 115°
  25. 35°
  26. 130°
  27. 55°
  28. 145°
  29. 100°
  30. 120°
  31. 45°
  32. 60°
  33. 65°
  34. 25°
  35. 60°
  36. 35°
  37. 55°
  38. 130°
  39. 70°
  40. 20°

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